# Thread: Movement of the field

1. ## Movement of the field

Find the movement of the field
$\displaystyle F(x,y) = (x^2-y)i + (x-y^2)j$

arrond the curve $\displaystyle \alpha$ which is the boundary of the region in 1° quedrant understood by coordinated axes and the circle $\displaystyle x^2+y^2=16$

My solution

$\displaystyle \int_0^{\frac{ \pi}{2}} (-64cos^2tsint +16sen^2t+16cos^2t-64sen^2tcost)dt = 8 \pi$

Correct ?

2. I figured again and got:

$\displaystyle 8 \pi \frac{128}{3}$

3. Originally Posted by Apprentice123
Find the movement of the field
$\displaystyle F(x,y) = (x^2-y)i + (x-y^2)j$

arrond the curve $\displaystyle \alpha$ which is the boundary of the region in 1° quedrant understood by coordinated axes and the circle $\displaystyle x^2+y^2=16$

My solution

$\displaystyle \int_0^{\frac{ \pi}{2}} (-64cos^2tsint +16sen^2t+16cos^2t-64sen^2tcost)dt = 8 \pi$

Correct ?

For this one you would want to use Greens' theorem:

$\displaystyle \iint_D 1-(-1)dA=2 \iint_D dA=2 \frac{1}{4}\pi (4)^2=8\pi$

4. Thank you